Question

Solve the following systems of inequalities graphically:

$2x+y\ge 8,x+2y\ge 10$

Answer 1

The given inequality is $2x+y\ge 8$.

Draw the graph of the line 2x+y=8.

Table of values satisfying the equation

2x+y=8

$\begin{array}{ccc}x& 3& 4\\ y& 2& 0\end{array}$

Putting (0,0) in the given inequation, we have $2\times 0+0\ge 8\Rightarrow 0\ge 8$, which is false

$\therefore$ Half plane of 2x+y $\ge$ 8 is away from origin.

Also the given inequality is $x+2y\ge 10$.

Draw the graph of the line x +2y =10.

Table of the values satisfying the equation x +2y =10

$\begin{array}{ccc}x& 2& 4\\ y& 4& 3\end{array}$

Putting (0,0) in the given inequation, we have $0+2\times 0\ge 10\Rightarrow 0\ge 10$, which is false.

$\therefore$ Half plane of $x+2y\ge 10$ is away from origin.